$g(n) = 6n$ $h(x) = -4x^{2}-4x-4(g(x))$ $f(t) = 4t+7+h(t)$ $ f(g(0)) = {?} $
Answer: First, let's solve for the value of the inner function, $g(0)$ . Then we'll know what to plug into the outer function. $g(0) = (6)(0)$ $g(0) = 0$ Now we know that $g(0) = 0$ . Let's solve for $f(g(0))$ , which is $f(0)$ $f(0) = (4)(0)+7+h(0)$ To solve for the value of $f$ , we need to solve for the value of $h(0)$ $h(0) = -4(0^{2})+(-4)(0)-4(g(0))$ To solve for the value of $h$ , we need to solve for the value of $g(0)$ $g(0) = (6)(0)$ $g(0) = 0$ That means $h(0) = -4(0^{2})+(-4)(0)+(-4)(0)$ $h(0) = 0$ That means $f(0) = (4)(0)+7$ $f(0) = 7$